Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits

Moment neural network and an efficient numerical method for modeling irregular spiking activity

Continuous rate-based neural networks have been widely applied to modeling the dynamics of cortical circuits. However, cortical neurons in the brain exhibit irregular spiking activity with complex correlation structures that cannot be captured by mean firing rate alone. To close this gap, we consider a framework for modeling irregular spiking activity, called the moment neural network, which naturally generalizes rate models to second-order moments and can accurately capture the firing statistics of spiking neural networks. We propose an efficient numerical method that allows for rapid evaluation of moment mappings for neuronal activations without solving the underlying Fokker-Planck equation. This allows simulation of coupled interactions of mean firing rate and firing variability of large-scale neural circuits while retaining the advantage of analytical tractability of continuous rate models. We demonstrate how the moment neural network can explain a range of phenomena including diverse Fano factor in networks with quenched disorder and the emergence of irregular oscillatory dynamics in excitation-inhibition networks with delay.

Distributed and dynamical communication: a mechanism for flexible cortico-cortical interactions and its functional roles in visual attention

Perceptual and cognitive processing relies on flexible communication among cortical areas; however, the underlying neural mechanism remains unclear. Here we report a mechanism based on the realistic spatiotemporal dynamics of propagating wave patterns in neural population activity. Using a biophysically plausible, multiarea spiking neural circuit model, we demonstrate that these wave patterns, characterized by their rich and complex dynamics, can account for a wide variety of empirically observed neural processes. The coordinated interactions of these wave patterns give rise to distributed and dynamic communication (DDC) that enables flexible and rapid routing of neural activity across cortical areas. We elucidate how DDC unifies the previously proposed oscillation synchronization-based and subspace-based views of interareal communication, offering experimentally testable predictions that we validate through the analysis of Allen Institute Neuropixels data. Furthermore, we demonstrate that DDC can be effectively modulated during attention tasks through the interplay of neuromodulators and cortical feedback loops. This modulation process explains many neural effects of attention, underscoring the fundamental functional role of DDC in cognition.

Chaotic neural dynamics facilitate probabilistic computations through sampling

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

Grid codes underlie multiple cognitive maps in the human brain

Grid cells fire at multiple positions that organize the vertices of equilateral triangles tiling a 2D space and are well studied in rodents. The last decade witnessed rapid progress in two other research lines on grid codes-empirical studies on distributed human grid-like representations in physical and multiple non-physical spaces, and cognitive computational models addressing the function of grid cells based on principles of efficient and predictive coding. Here, we review the progress in these fields and integrate these lines into a systematic organization. We also discuss the coordinate mechanisms of grid codes in the human entorhinal cortex and medial prefrontal cortex and their role in neurological and psychiatric diseases.

Chimera states in a chain of superdiffusively coupled neurons

Two- and three-component systems of superdiffusion equations describing the dynamics of action potential propagation in a chain of non-locally interacting neurons with Hindmarsh-Rose nonlinear functions have been considered. Non-local couplings based on the fractional Laplace operator describing superdiffusion kinetics are found to support chimeras. In turn, the system with local couplings, based on the classical Laplace operator, shows synchronous behavior. For several parameters responsible for the activation properties of neurons, it is shown that the structure and evolution of chimera states depend significantly on the fractional Laplacian exponent, reflecting non-local properties of the couplings. For two-component systems, an anisotropic transition to full incoherence in the parameter space responsible for non-locality of the first and second variables is established. Introducing a third slow variable induces a gradual transition to incoherence via additional chimera states formation. We also discuss the possible causes of chimera states formation in such a system of non-locally interacting neurons and relate them with the properties of the fractional Laplace operator in a system with global coupling.

Development of top-down cortical propagations in youth

Hierarchical processing requires activity propagating between higher- and lower-order cortical areas. However, functional neuroimaging studies have chiefly quantified fluctuations within regions over time rather than propagations occurring over space. Here, we leverage advances in neuroimaging and computer vision to track cortical activity propagations in a large sample of youth (n = 388). We delineate cortical propagations that systematically ascend and descend a cortical hierarchy in all individuals in our developmental cohort, as well as in an independent dataset of densely sampled adults. Further, we demonstrate that top-down, descending hierarchical propagations become more prevalent with greater demands for cognitive control as well as with development in youth. These findings emphasize that hierarchical processing is reflected in the directionality of propagating cortical activity and suggest top-down propagations as a potential mechanism of neurocognitive maturation in youth.

Natural gradient enables fast sampling in spiking neural networks

For animals to navigate an uncertain world, their brains need to estimate uncertainty at the timescales of sensations and actions. Sampling-based algorithms afford a theoretically-grounded framework for probabilistic inference in neural circuits, but it remains unknown how one can implement fast sampling algorithms in biologically-plausible spiking networks. Here, we propose to leverage the population geometry, controlled by the neural code and the neural dynamics, to implement fast samplers in spiking neural networks. We first show that two classes of spiking samplers-efficient balanced spiking networks that simulate Langevin sampling, and networks with probabilistic spike rules that implement Metropolis-Hastings sampling-can be unified within a common framework. We then show that careful choice of population geometry, corresponding to the natural space of parameters, enables rapid inference of parameters drawn from strongly-correlated high-dimensional distributions in both networks. Our results suggest design principles for algorithms for sampling-based probabilistic inference in spiking neural networks, yielding potential inspiration for neuromorphic computing and testable predictions for neurobiology.